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You can find lots of different gauges of hemp twine on Amazon with different colours. Cotton yarn for dishcloths and things is an option closer to your original idea.

I agree with everything @FloorCandy says. If you use a natural fiber they will be more durable and will probably carry the scent through better as well. Buy buy a few balls on sale to see how fast you go through it. You will be able to make 50 of those toys from a few small balls. And trust...